Problems of Modern Quantum Field Theory: Invited Lectures of the Spring School Held in Alushta Ussr, April 24 - May 5, 1989

ISBN-13: 9783540518334 / Angielski / Miękka / 1990 / 157 str.

Aleksandr A. Belavin; Anatolii U. Klimyk; Aleksandr B. Zamolodchikov

Opis

This volume is the compilation of invited lectures presented at the Spring School Problems of Modern Quantum Field Theory held in Alushta (USSR) April 24-May 5 1989, organized by the Institute for Theoretical Physics (Kiev) and Landau Institute for Theoretical Physics (Moscow). Approximately one hundred physicists and mathematicians attended lectures on aspects of mod- ern quantum field theory: Conformal Field Theory, Geometrical Quantization, Quantum Groups and Knizhnik-Zamolodchikov Equations, Non-Archimedian Strings, Calculations on Riemannian Surfaces. A number of experts active in research in these areas were present and they shared their ideas in both formal lectures and informal conversations. V. Drinfeld discusses the relation between quasi-Hopf algebras, conformal field theory, and knot invariants. The author sketches a new proof of Konno's theorem on the equivalence of the braid group representations corresponding to R-matrices and the Knizhnik-Zamolodchikov equation. The main ideas of quantum analogs of simple Lie superalgebras and their dual objects - algebras of functions on the quantum supergroup - are introduced in the paper by P.P. Kulish.He proposes the universal R-matrix for simplest superalgebra osp(2/1) and discusses the elements of a representation theory. In the paper by A. Alekseev and S. Shatashvili the correspondence between geometrical quantization and conformal field theory is established. It allows one to develop a Lagrange approach to two-dimensional conformal field theory. The authors also discuss the relation to finite R-matrices.

Spis treści

Quasi-Hopf Algebras and Knizhnik-Zamolodchikov Equations.- Quantum Lie Superalgebras and Supergroups.- From Geometric Quantization to Conformal Field Theory.- Bosonization of Wess-Zumino-Witten Models and Related Conformal Theories.- The Cutting and Sewing Method in String Theory.- P-Adic String World Sheets: Higher Genera.- Virasoro Action on Riemann Surfaces, Grassmannians, det $${\bar \partial _J}$$ and Segal-Wilson ?-Function.- On the Superextension of the Kadomtsev-Petviashvili Equation and Finite-Gap Solutions of Korteweg-de Vries Superequations.- Finite Size Effects in Conformal Field Theories and Non-local Operators in One-Dimensional Quantum Systems.- The Solution of the Two-Dimensional Ising Model with Magnetic Fields Applied to the Boundaries.- On the Relativistic Field Theories with Fractional Statistics and Spin in D=(2+1), (3+1).- Electron on a Surface in an External Magnetic Field: Hidden Supersymmetry, Zero Modes and Boundary Conditions.- Index of Contributors.